Galerkin Approximation of a Shielded Double-Sided Microstrip Line with Boundary Singularities

Signal conductors between two ground planes (i.e.. stripline transmission lines) and signal conductors above one ground plane (i.e., microstrip transmission line) serve as the means for propagating high-speed digital and analog signals on printed wiring boards (PWBs), and multichip modules (MCMs). For many important applications (e.g., wireless and other high speed technologies), the need for miniaturization requires that these high-speed electrical interconnections be provided on relatively dense PWBs and MCMs. This leads to design uncertainties concerning characteristic impedance and especially crosstalk. The purpose of this paper is to develop relatively simple formulas for computing the characteristic impedances and crosstalk of coupled stripline and microstrip transmission lines. Both unbalanced and balanced transmission lines are treated. The new formulas apply to both rectangular and circular conductors and are expressed in terms of the physical dimensions of the conductors and the effective dielectric constant of the medium. The formulas yield results which agree well with known results and experimental results.

Nowadays, demands for compactness, light weight, and broadband have a great impact on design issues at both component and system levels in wireless communications. Multilayered structures fabricated with low-temperature co-fired ceramic (LTCC) technologies have been developed recently in response to these demands. With this trend, double-sided printed circuits using conventional fabrication techniques with lower cost have been receiving plenty of attention. The parallel-strip line, belongs to the family of balanced transmission lines. The conventional printed circuit board technology is able to realize it easily. It is a simple structure comprised of a piece of dielectric substrate sandwiched by two conducting traces. Signals flowing on the upper and lower conductors are always equal in magnitude and 180° out of phase; therefore, parallel-strip line has an inherent advantage of easy realization of a balanced configuration. Balanced or double balanced microwave circuits, such as amplifier, mixer, and antenna, are frequently employed in high-performance wireless communications systems, and they can be directly fed by parallel-strip lines. In contrast, microstrip line is an unbalanced transmission line; therefore, extra effort of designing balanced to unbalanced structures (balun) is required for using microstrip transmission lines.

Open or short-circuit stubs in a strip (microstrip) transmission line are one of the most common elements of planar circuits used in numerous devices in the microwave frequency range: various types of filters, couplers, power amplifiers, antennas, sensors, wireless energy transfer systems, etc. Modern planar circuits in the microwave frequency range already contain stubs of a complex shape and a complex pattern inside the microstrip line. Therefore, an urgent problem is to develop an analyzing method for discontinuities in form of the closed or open stub in a microstrip transmission line at frequencies at which the transmission line theory already has significant errors and high-frequency effects must be considered. In paper a technique of scattering characteristics calculating on a symmetrical microstrip open stub by transverse resonance method is presented. Boundary value problems for a rectangular volume resonator based on a microstrip transmission line with a symmetric open stub are solved for three different boundary conditions in the plane of symmetry and on the longitudinal boundaries. To algebraize the boundary value problems for the resonator’s eigen frequencies with discontinuity, the corresponding two-dimensional functions of the magnetic potential are constructed, through which the components of the current density on the strip are calculated. The magnetic potential functions were written by decomposing them into series by orthogonal Chebyshev polynomials, which consider the behavior of the field on a thin edge and ensure fast convergence of the series and the algorithm. The developed algorithms were tested by calculating the scattering characteristics of a microstrip open stub using the transverse resonance method on the example of open stub in a microstrip transmission line with a resonant frequency of about 3.0 GHz. In addition, the method was tested on the example of numerical calculations of the dependence of resonant reflection frequencies of an open stub on its width.

This paper presents electromagnetic band gap (EBG)-based periodic microstrip lines and balanced (differential) microstrip lines. Specifically, it is shown that through a proper modulation of the strip width in a microstrip transmission line, a stopband with controllable characteristics can be obtained. These EBG structures are then applied to differential microstrip lines, where it is shown that it is possible to achieve common-mode rejection in a certain frequency band, keeping the differential signals unaltered in that band. This is an interesting approach to implement common-mode suppressed differential microstrip lines without ground plane etching.

Open stubs in a strip (microstrip) transmission line are one of the most common elements of planar circuits used in numerous devices in the various types of wireless systems. Therefore, the urgent problem is to develop an analyzing method for discontinuities in the form of the open stub in a microstrip transmission line at frequencies at which the high-frequency effects must be considered. In the paper, a technique of scattering characteristics calculating on a symmetrical microstrip open stub by transverse resonance method is presented. Boundary value problems for a rectangular volume resonator based on a microstrip transmission line with a symmetric open stub are solved for the three options boundary conditions in the symmetry plane and on the longitudinal boundaries. The intersection of the spectral curves obtained by the numerical solution of the “electric” and “magnetic” boundary value problems determines the minima of a reflection or transmission coefficients of fundamental wave on discontinuities. To algebraize the boundary value problems for the eigen frequencies of volume resonator with discontinuity, the corresponding two-dimensional functions of the magnetic potential are constructed, through which the components of the current density on the strip are determined. The functions of magnetic potential were defined by decomposing them into expansion by Fourier series, which ensures stable convergence of the series and numerical calculation algorithm. The developed technique has been tested by calculating the eigenfrequency spectra of an open microstrip stub using the transverse resonance method on the example of an open stub in a microstrip transmission line with a resonant frequency of about 3.0 GHz. Also, a technique for numerical solutions of “electric” and “magnetic” boundary-value problems for resonators with two electrodynamically coupled symmetric open stubs in a microstrip transmission line is developed.

For a high‐density multilayer substrate ALIVH, balanced pair transmission lines on which 60‐GHz signals can be transmitted are proposed. First, it is shown that transmission of millimeter wave signals is difficult due to impedance mismatch of the vias in the conventional unbalanced transmission lines. Further, it is shown that transmission at up to 90 GHz is possible by a design such that the microstrip line on the surface, the strip line in the inner layer, and the vias connecting each layer have the same transmission line spacing and the same characteristic impedance. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 89(10): 1–8, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20249

The effect of a conductive substrate, such as silicon, on the attenuation of microstrip (MS) lines has been investigated in the past. No such treatment exists for coplanar (CPW) lines, and experimental data on the additional attenuation due to a finite conductivity of the substrate is extremely scarce. Using basic transmission line theory, simple expressions have been derived for the losses caused by a conductive substrate for both the coplanar and the microstrip lines. For microstrip lines, good agreement is obtained with previously published theoretical and experimental data on conducting silicon substrates. In contrast to the case for microstrip lines, where the conductive substrate losses are independent of the line impedance, a dependence is found for coplanar lines.

A comparative analysis of MIMO communications based on physical measurements of balanced and unbalanced transmission line channels is presented. Specifically, the effect of imperfect knowledge of the channel is considered. The novel contribution of this work lies in the fact that measurements of far end crosstalk signal paths and transmission line signal paths on unbalanced transmission lines over a frequency range from 300 kHz to 100 MHz will be incorporated into this analysis. Also, this work presents a comparative capacity analysis of MIMO communications systems based on balanced transmission line channels and unbalanced transmission line channels where the extent of imperfect knowledge of the channel is quantified by the variance of the complex normally distributed scalar elements of a matrix and this has not been reported in literature to date. The physical measurements on the unbalanced transmission lines are offered here as being indicative of poor quality transmission lines where crosstalk levels and insertion losses are so significant that these poor quality transmission lines would be deemed out-of-range for high speed internet connections.

Analytical expressions for the near‐end voltages are derived from the unit‐cell of strong‐coupled transmission lines (TLs) and validated with simulations and measurements. The two TLs investigated here are the microstrip TL and a complementary split ring resonator (CSRR) loaded TL on a printed circuit board. This work is then used to develop spacing guidelines and investigate new methods (beyond weakly‐coupled TLs) to reduce the coupling for designers that may use CSRR loaded TLs in very close proximity of other microstrip TLs.

ABSTRACTThis paper focuses on the design, fabrication and analysis of a periodically loaded transmission line (PLTL) within a homogenous medium. The proposed method aims to mitigate near‐end crosstalk (NEXT) and far‐end crosstalk (FEXT) improve the overall transmission performance for digital signal data transmission over a frequency range of 1 to 14 GHz. The periodic loading is designed to optimize the coupling ratios between capacitive and inductive components, leading to a more balanced and efficient microstrip transmission line. Unlike traditional microstrip configurations, the PLTLs in a homogeneous medium offer improved impedance matching and reduced signal distortion. This study employs full‐wave simulations to analyze the performance of the proposed PLTLs and provides a comprehensive comparison with conventional microstrip transmission line design. The key parameters include insertion loss , near‐end crosstalk , and far‐end crosstalk are 0.535, 30.651, and 44.695 dB, respectively, evaluated to assess the defected microstrip structure (DMS) effectiveness in accommodating the digital signals. The experimental results are compared with the simulation outcomes to validate the accuracy of the proposed design.

Applied Electromagnetics and Electromagnetic Compatibility

This article presents an analysis of metamaterial resonators coupled with microstrip transmission line. The behavior of complementary electric-LC resonators loaded on a microstrip line is analyzed using the equivalent circuit model. In this paper, it is shown that a special type of these resonators show a dual-mode behavior when excited through the electromagnetic field around the microstrip transmission lines. The bandstop and bandpass configurations of these dual mode resonators loaded with microstrip lines are introduced and analyzed. Their potential applications are highlighted through designing a displacement sensor and a dual-mode bandpass filter prototypes.

An ultra‐compact spoof surface plasmon polariton (UCSSPP) transmission line (TL) based on a meander line is proposed, which can achieve almost the same transmission performance as the conventional rectangular‐groove SSPP TL, but the linewidth is greatly reduced by more than 40%. The coupling effect between two UCSSPP TLs in different line arrangements has been well studied, revealing that excellent crosstalk suppression can be achieved when two TLs are arranged back‐to‐back, while strong coupling occurs when they are arranged face‐to‐back or face‐to‐face. The signal integrity of back‐to‐back UCSSPP TLs is analyzed and demonstrated, which shows that the signal integrity can be greatly improved compared with microstrip (MS) TLs. In addition, based on the principle of mode mismatch, MS and UCSSPP TLs are arranged alternately to solve the mutual coupling problem in multi‐line systems. In contrast, benefiting from the strong coupling of face‐to‐face UCSSPP TLs, an ultra‐miniaturized SSPP coupler working at 9 GHz is designed, whose size can be reduced by over 75% compared with conventional MS coupler. The measurement results show good agreement with full‐wave simulations, indicating that the proposed UCSSPP TL has significant advantages in signal integrity and device miniaturization over previously reported SSPP TLs.

In this study the changes in the resonance frequencies of horizontally and vertically positioned split ring resonator (SRR) and double sided split ring resonator (DSRR) layered structures, which are excited by microstrip transmission line, depending on the dielectric constant and the thickness of the material under test (MUT) and the location of the split at the resonator relative to the transmission line has been observed and the sensitivity analyses have been carried out. According to this, vertically positioned resonator structures are shown to be more sensitive than the horizontally positioned ones considering the resonance response with respect to the changes of MUT dielectric constant. In the meantime, it has been revealed that the sensitivity performances of the studied structures are dependent on the MUT dielectric constant range and the MUT thickness. These results are important for microwave sensor applications which is a trend topic.

A fully automated tool for designing CRLH interdigital microstrip structures using a co-design synthesis computational approach is proposed and demonstrated experimentally. This approach uses an electromagnetic simulator in conjunction with a genetic algorithm to synthesize and optimize a balanced CRLH interdigital microstrip transmission line. The high sensitivity of a long balanced transmission line to fabrication tolerances is controlled by the use of a high precision 3D simulator. The 2.5D simulator used was found insufficient for a large number of unit cells. A 13 UC CRLH transmission line is designed with the proposed approach. The response sensitivity of the balanced transmission lines to the over/under-etching factor is highlighted by comparing the measurements of four lines with different factors. The effect of over/under-etching is significant for values larger than 10 μm.